Reflected fluxes for broken clouds over a Lambertian surface

Reflected fluxes are calculated for broken cloudiness (i.e., nonplane parallel) as a function of cloud cover, cloud optical depth, solar zenith angle and surface albedo. These calculations extend previous results for broken cloud reflected fluxes over a black surface. The present study demonstrates that not only radiances but also radiative fluxes over high albedo surfaces may be decreased by the presence of broken cloudiness. Conventional wisdom states that cloud radiances (brightnesses) are always greater than the background. While most cloud retrieval schemes are built around this assumption, it is incorrect for clouds over high albedo surfaces such as found in polar regions. However, the most startling and counterintuitive conclusion of this study is that nonabsorbing finite clouds over a highly reflecting surface will decrease the system albedo. As a result, surface absorption is increased, the result of multiple scattering between surface and cloud layer, controlled by cloud morphology and cloud optical thickness. A simple parameterization of the effects of cloud contamination upon retrieved albedo is given in terms of solar zenith angle, cloud optical depth, surface albedo, cloud cover, and plane-parallel cloud albedo. In this way, the effects of broken cloudiness are modeled in terms of easily computed plane-parallel values.